Summary: q Breathers in Finite Lattices: Nonlinearity and Weak Disorder
M. V. Ivanchenko
Department of Applied Mathematics, University of Leeds, LS2 9JT, Leeds, United Kingdom
(Received 3 December 2008; published 30 April 2009)
Nonlinearity and disorder are the recognized ingredients of the lattice vibrational dynamics, the factors
that could be diminished, but never excluded. We generalize the concept of q breathers--periodic orbits in
nonlinear lattices, exponentially localized in the linear mode space--to the case of weak disorder, taking
the Fermi-Pasta-Ulan chain as an example. We show that these nonlinear vibrational modes remain
exponentially localized near the central mode and stable, provided the disorder is sufficiently small. The
instability threshold depends sensitively on a particular realization of disorder and can be modified by
specifically designed impurities. Based on this sensitivity, an approach to controlling the energy flow
between the modes is proposed. The relevance to other model lattices and experimental miniature arrays is
discussed.
DOI: 10.1103/PhysRevLett.102.175507 PACS numbers: 63.20.Pw, 05.45.Àa, 63.20.Ry
Nonlinearity and disorder are ubiquitous and unavoid-
able features of discrete extended systems, the key players
in a wealth of fundamental dynamical and statistical physi-
cal phenomena such as thermalization, thermal conductiv-
ity, wave propagation, electron and phonon scattering.
Lattice vibrational modes are central to these processes.